.
be the midpoint of the arc 
not containing 
and define 
similarly. Show that the orthocenter of 
is the incenter 
of 
can be written in the form![\[
\frac{\sqrt[3]{a} + \sqrt[3]{b} + 1}{c},
\]](http://latex.artofproblemsolving.com/9/e/9/9e96c07ea3b0750af8bed344df6e8a86fcf0d772.png)
where 
and 
are positive integers. Find the value of 
.
such that 
divides 
.
Y by Adventure10, Mango247
In a triangle 
let 
be the midpoint of side 
. Draw circles with centers 
and radii 
respectively and let 
be their common chord. Similarly denote the segments 
and 
. Show that lines 
and are concurrent.
let 
be the midpoint of side 
. Draw circles with centers 
and radii 
respectively and let 
be their common chord. Similarly denote the segments 
and 
. Show that lines 
and are concurrent.
